PCA eigenvector/eigenvalue help

Hey, I would like to calculate PC1 PC2 and PC3 of this 3D loop (show attached picture). It's 3angles plotted together /time. Someone already helped me finding a few things but Ultimatly I would like to know the value of the 3 first eigenvectors and there direction. Thx for any help.

Answer 1

[TED MOSBY]

Hi,

To compute the first three principal components you need the numeric time-series of your three joint angles (thigh, shank, foot). Assuming you have 3 vectors such that:

thighAngle  :  N-by-1
shankAngle  :  N-by-1
footAngle   :  N-by-1

Once you have those three columns, PCA is straightforward:

X = [thighAngle(:)  shankAngle(:)  footAngle(:)];
Xm   = X - mean(X,1);

% 2.  Run PCA  (Statistics & ML Toolbox)
[coeff, score, latent, ~, explained, mu] = pca(X);   % ‘coeff’ are the eigenvectors

PC1_dir = coeff(:,1);       % unit-length direction of the first PC
PC2_dir = coeff(:,2);
PC3_dir = coeff(:,3);

PC1_eig = latent(1);        % eigenvalue (variance captured by PC1)
PC2_eig = latent(2);
PC3_eig = latent(3);

PC1_score = score(:,1);     % time-series of the loop projected onto PC1

Here is the documentation of PCA:

https://www.mathworks.com/help/stats/pca.html?s_tid=srchtitle_support_results_1_latent+pca#

Hope this helps!